Conceptually, The Invisible Library may be the best book ever, in that it's about a Library between the worlds which sends out its Librarians to gather unique works of fiction from them. It's a book about the biggest, twistiest, scariest library ever, and the people who work for it. By all rights it should be fantastic.
Unfortunately, we don't actually see all that much of the Library: instead, we get a vaguely steampunkish adventure in which Irene, a fairly junior Librarian, and her young mentee Kai (who is, of course, Super Hot) try to steal a rare copy of Grimms' Fairy Tales from an alternative version of London. Things go badly, of course: there is evil magic at work in the world, and a shadow from the Library's past manages to loom over the mission, without actually telling us anything about that past.
Still, all this would be fine if Cogman's writing was good, but it isn't, really. Irene's characterization isn't particularly strong; nor is Kai's, or anyone else's for that matter. There's a much too heavy reliance on conveniently placed violence ("a bad thing would have happened, if a giant centipede hadn't arrived outside the restaurant!" Not an actual quote, but you get the idea) and other dramatic clichés, like the villain revealing his whole plan at the end, or the heroine coming up with a Dangerous Plan which Might Just Work! (It always does, needless to say.) Plus, the system of magic which the Librarians use, the Language (think Eragon: the Language is the language of truth, essentially) is OK in principle, but in practice feels a bit underdeveloped: it's telegraphed through bolding words, which interrupts the flow of the text, and despite the fact that it's supposed to be about precision and description Cogman's use of it is very workaday. It's like she sets up all these rules for using it and then appends so many "yes, buts" that those rules didn't really need to exist in the first place.
I guess your mileage may vary - if you particularly like steampunk and are in the mood for a light, quick read with lots of action and adventure you'll probably enjoy The Invisible Library. I might have enjoyed it had it caught me at a better time. Just be aware that it's not as much about books as it claims to be.